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Search for eta(c)(2S)h(c) -> p(p)over-bar decays and measurements of the chi(cJ) -> p(p)over-bar branching fractions

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arXiv:1310.6099v2 [hep-ex] 12 Feb 2015

Search for the η

c

(2S)/h

c

p ¯

p decays and measurements of the

χ

cJ

p ¯

p branching fractions

M. Ablikim1, M. N. Achasov8,a, X. C. Ai1, O. Albayrak4, D. J. Ambrose41, F. F. An1,

Q. An42, J. Z. Bai1, R. Baldini Ferroli19A, Y. Ban28, J. V. Bennett18, M. Bertani19A, J. M. Bian40, E. Boger21,b, O. Bondarenko22, I. Boyko21, S. Braun37, R. A. Briere4,

H. Cai47, X. Cai1, O. Cakir36A, A. Calcaterra19A, G. F. Cao1, S. A. Cetin36B, J. F. Chang1,

G. Chelkov21,b, G. Chen1, H. S. Chen1, J. C. Chen1, M. L. Chen1, S. J. Chen26,

X. Chen1, X. R. Chen23, Y. B. Chen1, H. P. Cheng16, X. K. Chu28, Y. P. Chu1,

D. Cronin-Hennessy40, H. L. Dai1, J. P. Dai1, D. Dedovich21, Z. Y. Deng1, A. Denig20,

I. Denysenko21, M. Destefanis45A,45C, W. M. Ding30, Y. Ding24, C. Dong27, J. Dong1,

L. Y. Dong1, M. Y. Dong1, S. X. Du49, J. Fang1, S. S. Fang1, Y. Fang1, L. Fava45B,45C,

C. Q. Feng42, C. D. Fu1, J. L. Fu26, O. Fuks21,b, Q. Gao1, Y. Gao35, C. Geng42,

K. Goetzen9, W. X. Gong1, W. Gradl20, M. Greco45A,45C, M. H. Gu1, Y. T. Gu11,

Y. H. Guan1, A. Q. Guo27, L. B. Guo25, T. Guo25, Y. P. Guo27, Y. P. Guo20, Y. L. Han1,

F. A. Harris39, K. L. He1, M. He1, Z. Y. He27, T. Held3, Y. K. Heng1, Z. L. Hou1, C. Hu25,

H. M. Hu1, J. F. Hu37, T. Hu1, G. M. Huang5, G. S. Huang42, J. S. Huang14, L. Huang1,

X. T. Huang30, Y. Huang26, T. Hussain44, C. S. Ji42, Q. Ji1, Q. P. Ji27, X. B. Ji1, X. L. Ji1,

L. L. Jiang1, X. S. Jiang1, J. B. Jiao30, Z. Jiao16, D. P. Jin1, S. Jin1, F. F. Jing35,

T. Johansson46, N. Kalantar-Nayestanaki22, X. L. Kang1, M. Kavatsyuk22, B. Kloss20,

B. Kopf3, M. Kornicer39, W. Kuehn37, A. Kupsc46, W. Lai1, J. S. Lange37, M. Lara18,

P. Larin13, M. Leyhe3, C. H. Li1, Cheng Li42, Cui Li42, D. Li17, D. M. Li49, F. Li1,

G. Li1, H. B. Li1, J. C. Li1, K. Li30, K. Li12, Lei Li1, P. R. Li38, Q. J. Li1, T. Li30,

W. D. Li1, W. G. Li1, X. L. Li30, X. N. Li1, X. Q. Li27, X. R. Li29, Z. B. Li34, H. Liang42,

Y. F. Liang32, Y. T. Liang37, G. R. Liao35, D. X. Lin13, B. J. Liu1, C. L. Liu4, C. X. Liu1,

F. H. Liu31, Fang Liu1, Feng Liu5, H. B. Liu11, H. H. Liu15, H. M. Liu1, J. Liu1, J. P. Liu47,

K. Liu35, K. Y. Liu24, P. L. Liu30, Q. Liu38, S. B. Liu42, X. Liu23, Y. B. Liu27, Z. A. Liu1,

Zhiqiang Liu1, Zhiqing Liu20, H. Loehner22, X. C. Lou1,c, G. R. Lu14, H. J. Lu16, H. L. Lu1,

J. G. Lu1, X. R. Lu38, Y. Lu1, Y. P. Lu1, C. L. Luo25, M. X. Luo48, T. Luo39, X. L. Luo1,

M. Lv1, F. C. Ma24, H. L. Ma1, Q. M. Ma1, S. Ma1, T. Ma1, X. Y. Ma1, F. E. Maas13,

M. Maggiora45A,45C, Q. A. Malik44, Y. J. Mao28, Z. P. Mao1, J. G. Messchendorp22, J. Min1, T. J. Min1, R. E. Mitchell18, X. H. Mo1, Y. J. Mo5, H. Moeini22, C. Morales

Morales13, K. Moriya18, N. Yu. Muchnoi8,a, Y. Nefedov21, I. B. Nikolaev8,a, Z. Ning1,

S. Nisar7, X. Y. Niu1, S. L. Olsen29, Q. Ouyang1, S. Pacetti19B, M. Pelizaeus3,

H. P. Peng42, K. Peters9, J. L. Ping25, R. G. Ping1, R. Poling40, E. Prencipe20, M. Qi26,

S. Qian1, C. F. Qiao38, L. Q. Qin30, X. S. Qin1, Y. Qin28, Z. H. Qin1, J. F. Qiu1,

K. H. Rashid44, C. F. Redmer20, M. Ripka20, G. Rong1, X. D. Ruan11, A. Sarantsev21,d,

K. Sch¨onning46, S. Schumann20, W. Shan28, M. Shao42, C. P. Shen2, X. Y. Shen1,

H. Y. Sheng1, M. R. Shepherd18, W. M. Song1, X. Y. Song1, S. Spataro45A,45C, B. Spruck37,

G. X. Sun1, J. F. Sun14, S. S. Sun1, Y. J. Sun42, Y. Z. Sun1, Z. J. Sun1, Z. T. Sun42,

C. J. Tang32, X. Tang1, I. Tapan36C, E. H. Thorndike41, D. Toth40, M. Ullrich37,

I. Uman36B, G. S. Varner39, B. Wang27, D. Wang28, D. Y. Wang28, K. Wang1, L. L. Wang1,

L. S. Wang1, M. Wang30, P. Wang1, P. L. Wang1, Q. J. Wang1, S. G. Wang28, W. Wang1,

X. F. Wang35, Y. D. Wang19A, Y. F. Wang1, Y. Q. Wang20, Z. Wang1, Z. G. Wang1,

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Z. H. Wang42, Z. Y. Wang1, D. H. Wei10, J. B. Wei28, P. Weidenkaff20, S. P. Wen1,

M. Werner37, U. Wiedner3, M. Wolke46, L. H. Wu1, N. Wu1, W. Wu27, Z. Wu1, L. G. Xia35,

Y. Xia17, D. Xiao1, Z. J. Xiao25, Y. G. Xie1, Q. L. Xiu1, G. F. Xu1, L. Xu1, Q. J. Xu12,

Q. N. Xu38, X. P. Xu33, Z. Xue1, L. Yan42, W. B. Yan42, W. C. Yan42, Y. H. Yan17,

H. X. Yang1, Y. Yang5, Y. X. Yang10, H. Ye1, M. Ye1, M. H. Ye6, B. X. Yu1, C. X. Yu27,

H. W. Yu28, J. S. Yu23, S. P. Yu30, C. Z. Yuan1, W. L. Yuan26, Y. Yuan1, A. A. Zafar44,

A. Zallo19A, S. L. Zang26, Y. Zeng17, B. X. Zhang1, B. Y. Zhang1, C. Zhang26,

C. B. Zhang17, C. C. Zhang1, D. H. Zhang1, H. H. Zhang34, H. Y. Zhang1, J. J. Zhang1,

J. L. Zhang1, J. Q. Zhang1, J. W. Zhang1, J. Y. Zhang1, J. Z. Zhang1, S. H. Zhang1,

X. J. Zhang1, X. Y. Zhang30, Y. Zhang1, Y. H. Zhang1, Z. H. Zhang5, Z. P. Zhang42,

Z. Y. Zhang47, G. Zhao1, J. W. Zhao1, Lei Zhao42, Ling Zhao1, M. G. Zhao27, Q. Zhao1,

Q. W. Zhao1, S. J. Zhao49, T. C. Zhao1, X. H. Zhao26, Y. B. Zhao1, Z. G. Zhao42,

A. Zhemchugov21,b, B. Zheng43, J. P. Zheng1, Y. H. Zheng38, B. Zhong25, L. Zhou1,

Li Zhou27, X. Zhou47, X. K. Zhou38, X. R. Zhou42, X. Y. Zhou1, K. Zhu1, K. J. Zhu1,

X. L. Zhu35, Y. C. Zhu42, Y. S. Zhu1, Z. A. Zhu1, J. Zhuang1, B. S. Zou1, J. H. Zou1

(BESIII Collaboration)

1 Institute of High Energy Physics, Beijing 100049, People’s Republic of China 2 Beihang University, Beijing 100191, People’s Republic of China

3 Bochum Ruhr-University, D-44780 Bochum, Germany

4 Carnegie Mellon University, Pittsburgh, Pennsylvania 15213, USA 5 Central China Normal University, Wuhan 430079, People’s Republic of China

6 China Center of Advanced Science and Technology,

Beijing 100190, People’s Republic of China

7 COMSATS Institute of Information Technology,

Lahore, Defence Road, Off Raiwind Road, 54000 Lahore

8 G.I. Budker Institute of Nuclear Physics SB RAS (BINP), Novosibirsk 630090, Russia 9 GSI Helmholtzcentre for Heavy Ion Research GmbH, D-64291 Darmstadt, Germany

10 Guangxi Normal University, Guilin 541004, People’s Republic of China 11 GuangXi University, Nanning 530004, People’s Republic of China 12 Hangzhou Normal University, Hangzhou 310036, People’s Republic of China 13 Helmholtz Institute Mainz, Johann-Joachim-Becher-Weg 45, D-55099 Mainz, Germany

14 Henan Normal University, Xinxiang 453007, People’s Republic of China

15Henan University of Science and Technology, Luoyang 471003, People’s Republic of China 16 Huangshan College, Huangshan 245000, People’s Republic of China

17 Hunan University, Changsha 410082, People’s Republic of China 18 Indiana University, Bloomington, Indiana 47405, USA 19 (A)INFN Laboratori Nazionali di Frascati, I-00044, Frascati,

Italy; (B)INFN and University of Perugia, I-06100, Perugia, Italy

20 Johannes Gutenberg University of Mainz,

Johann-Joachim-Becher-Weg 45, D-55099 Mainz, Germany

21 Joint Institute for Nuclear Research, 141980 Dubna, Moscow region, Russia 22 KVI, University of Groningen, NL-9747 AA Groningen, Netherlands

23 Lanzhou University, Lanzhou 730000, People’s Republic of China

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24 Liaoning University, Shenyang 110036, People’s Republic of China 25 Nanjing Normal University, Nanjing 210023, People’s Republic of China

26 Nanjing University, Nanjing 210093, People’s Republic of China 27 Nankai university, Tianjin 300071, People’s Republic of China 28 Peking University, Beijing 100871, People’s Republic of China

29 Seoul National University, Seoul, 151-747 Korea

30 Shandong University, Jinan 250100, People’s Republic of China 31 Shanxi University, Taiyuan 030006, People’s Republic of China 32 Sichuan University, Chengdu 610064, People’s Republic of China

33 Soochow University, Suzhou 215006, People’s Republic of China 34 Sun Yat-Sen University, Guangzhou 510275, People’s Republic of China

35 Tsinghua University, Beijing 100084, People’s Republic of China

36 (A)Ankara University, Dogol Caddesi, 06100 Tandogan, Ankara, Turkey; (B)Dogus

University, 34722 Istanbul, Turkey; (C)Uludag University, 16059 Bursa, Turkey

37 Universitaet Giessen, D-35392 Giessen, Germany

38 University of Chinese Academy of Sciences, Beijing 100049, People’s Republic of China 39 University of Hawaii, Honolulu, Hawaii 96822, USA

40 University of Minnesota, Minneapolis, Minnesota 55455, USA 41 University of Rochester, Rochester, New York 14627, USA

42 University of Science and Technology of China, Hefei 230026, People’s Republic of China 43 University of South China, Hengyang 421001, People’s Republic of China

44 University of the Punjab, Lahore-54590, Pakistan

45 (A)University of Turin, I-10125, Turin, Italy; (B)University of Eastern

Piedmont, I-15121, Alessandria, Italy; (C)INFN, I-10125, Turin, Italy

46 Uppsala University, Box 516, SE-75120 Uppsala

47 Wuhan University, Wuhan 430072, People’s Republic of China 48 Zhejiang University, Hangzhou 310027, People’s Republic of China 49 Zhengzhou University, Zhengzhou 450001, People’s Republic of China

a Also at the Novosibirsk State University, Novosibirsk, 630090, Russia b Also at the Moscow Institute of Physics and Technology, Moscow 141700, Russia

c Also at University of Texas at Dallas, Richardson, Texas 75083, USA d Also at the PNPI, Gatchina 188300, Russia

(Dated: February 15, 2015)

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Abstract

Using a sample of 1.06 × 108 ψ(3686) events collected with the BESIII detector at BEPCII, the

decays ηc(2S) → p¯p and hc → p¯p are searched for, where ηc(2S) and hc are reconstructed in the

decay chains ψ(3686) → γηc(2S), ηc(2S) → p¯p and ψ(3686) → π0hc, hc → p¯p, respectively. No

significant signals are observed. The upper limits of the product branching fractions are determined

to be B(ψ(3686) → γηc(2S)) × B(ηc(2S) → p¯p) < 1.4 × 10−6 and B(ψ(3686) → π0hc) × B(hc →

p) < 1.3 × 10−7 at the 90% C.L.. The branching fractions for χ

cJ → p¯p (J = 0, 1, 2) are also

measured to be (24.5 ± 0.8 ± 1.3, 8.6 ± 0.5 ± 0.5, 8.4 ± 0.5 ± 0.5) × 10−5

, which are the world’s most precise measurements.

PACS numbers: 13.25.Gv, 13.40.Hq, 14.40.Pq

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I. INTRODUCTION

Charmonium has been playing an important role in understanding the dynamics of QCD. Despite the success of QCD in many aspects of the strong interaction, the charmonium decay mechanism remains challenging and presents disagreement between experimental data and theoretical predictions [1].

In massless QCD models, the processes ηc/χc0/hc/ηc(2S) → p¯p are forbidden by the

helicity selection rule [2]. However, the experimental observations of the decays ηc/χc0 →

p¯p [3], as well as hcformed in the p¯p annihilation [4], indicate substantial contributions due to

finite masses. These observations have stimulated many theoretical efforts [5–7]. In Ref. [8], it is pointed out that the branching fraction of ηc(2S) → p¯p with respect to that of ηc → p¯p

may serve as a criterion to validate the helicity conservation theorem, and an anomalous decay in ηc(2S) might imply the existence of a glueball. For the decay hc → p¯p, possible

large branching fractions are suggested. Authors of Ref. [5] investigate the long distance contribution via charmed hadron loops and predict B(hc → p¯p) = (1.52 − 1.93) × 10−3. In

Ref. [6], a branching fraction of B(hc → p¯p) = (3.2±0.5)×10−3is predicted by “factorizing”

the initial and the final states.

In this paper, we report on a search for ηc(2S) and hc decays into p¯p, where ηc(2S)

is produced from the ψ(3686) radiative transition, while hc is produced via the

isospin-forbidden process ψ(3686) → π0h

c. In addition, we measure the decays χcJ → p¯p with J =

0, 1, and 2. The analysis is based on an e+e

annihilation sample of 1.06 × 108 events taken

at √s = 3.686 GeV [9]. A 44 pb−1 sample taken at √s = 3.65 GeV is used to estimate the background contribution from the continuum processes.

II. EXPERIMENT AND DATA SETS

The BESIII detector, described in detail in Ref. [10], has an effective geometrical accep-tance of 93% of 4π. A helium-based main drift chamber (MDC) determines the momentum of charged particles measured in a 1 T magnetic field with a resolution 0.5% at 1 GeV/c (the resolutions mentioned in the paper are rms resolutions). The energy loss (dE/dx) is also measured with a resolution better than 6%. An electromagnetic calorimeter (EMC) mea-sures energies and positions of electrons and photons. For 1.0 GeV photons and electrons, the energy resolution is 2.5% in the barrel and 5.0% in the end caps, and the position reso-lution is 6 mm in the barrel and 9 mm in the end caps. A time-of-flight system (TOF) with a time resolution of 80 ps (110 ps) in the barrel (end cap) is used for particle identification. A muon chamber based on resistive plate chambers with 2 cm position resolution provides information for muon identification.

An inclusive Monte Carlo (MC) sample of 1.06 × 108 ψ(3686) events is used for

back-ground studies. The ψ(3686) resonance is produced by the event generator KKMC [11], and the decays are generated by EvtGen [12] with known branching fractions [3], while the unmeasured decays are generated according to the Lundcharm model [13]. Exclusive signal MC samples are generated to determine the detection efficiency and to optimize selection criteria. The hc → p¯p and ηc(2S) → p¯p decays are generated according to phase space

distributions, and χcJ → p¯p decays are generated with an angular distribution of protons

following the form 1 + α cos2θ in the χ

cJ helicity frame, where α is taken from measured

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data. GEANT4 is used to simulate events where the measured detector resolutions are taken into consideration [14].

III. EVENT SELECTION AND BACKGROUND ANALYSIS

Each charged track is required to have its point of closest approach to the beam line within 1 cm of the beam line in the radial direction and within 10 cm from the interaction point along the beam direction and to lie within the polar angle coverage of the MDC, | cos θ| < 0.93 in laboratory frame. The information from the TOF is used to form a likelihood Lp (LK/Lπ) with a proton (kaon/pion) hypothesis. To identify a track as a

proton, the likelihood Lp is required to be greater than LK and Lπ.

Photons are reconstructed from isolated showers in the EMC which are at least 15 (25) degrees away from the proton (antiproton) candidate. Photon candidates in the barrel (| cos θ| < 0.8) and in the end cap (0.86 < | cos θ| < 0.92) must have an energy of at least 25 MeV. Electromagnetic showers close to the EMC boundaries are poorly reconstructed and excluded from this analysis. To suppress electronic noise and energy deposits unrelated to the event, the EMC timing of the photon candidate must be in coincidence with collision events 0 ≤ t ≤ 14 (in units of 50 ns).

In the ψ(3686) → γηc(2S)/χcJ → γp¯p and ψ(3686) → π0hc → π0p¯p → γγp¯p selection,

the candidate events must have two oppositely charged tracks and at least one or two good photons, respectively. To suppress the nonproton backgrounds in selecting the γp¯p final states, both tracks are required to be positively identified as protons, while for the γγp¯p final states only one track is required to be a proton. A four-constraint (4C) kinematic fit of γp¯p (γγp¯p) candidates is performed to the total initial four-momentum of the colliding beams in order to reduce background and to improve the mass resolution. If more photons than required exist in an event, the best one(s) is(are) selected by minimizing the χ24C of the 4C kinematic fit. Events with χ2

4C < 40 are accepted as γp¯p (γγp¯p) candidates. For γγp¯p

candidates, the invariant mass of the two selected photons is further required to be in the range 0.11 GeV/c2 < M(γγ) <0.15 GeV/c2.

For the ψ(3686) → γηc(2S)/χcJ → γp¯p channel, the main backgrounds in the ηc(2S)

signal region (3.6 GeV/c2 ≤ M(p¯p) ≤ 3.66 GeV/c2) are ψ(3686) → p¯p decays combined

with a fake photon, or with a photon from initial-state radiation or final-state radiation (FSR) and the continuum process. In the χcJ signal region (3.3 GeV/c2 ≤ M(p¯p) ≤ 3.6

GeV/c2), the main backgrounds come from the decays ψ(3686) → π0p or the nonresonant

process ψ(3686) → γp¯p. Since the energy of the transition photon from ψ(3686) → γηc(2S)

is only 50 MeV, ψ(3686) → p¯p events can easily fake signal events by combining with a fake photon. With a 4C kinematic fit, those events will produce a peak in the p¯p mass spectrum close to the expected ηc(2S) mass. Therefore, a three-constraint (3C) kinematic fit, where

the magnitude of the photon momentum is allowed to float, is used to determine signal yields. The 3C fit keeps the ψ(3686) → p¯p peak at the correct position as the photon momentum tends to zero, and it can separate this background from the ηc(2S) signal efficiently as shown

in Fig. 1 [15]. The background from the continuum process is studied with the data taken at√s = 3.65 GeV. The contribution of the background is found to be negligible.

Background from ψ(3686) → π0p is measured by selecting π0p events from data. The

π0p selection is the same as that for ψ(3686) → π0h

c, hc → p¯p. A MC sample of ψ(3686) →

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) 2 (GeV/c p p M 3.6 3.61 3.62 3.63 3.64 3.65 3.66 3.67 3.68 3.69 3.7 ) 2 Events/ (2 MeV/c 0 100 200 300 400 500 600 700 800 900 1000 (2S) c η γ (3686)-> ψ 3C for (2S) c η γ (3686)-> ψ 4C for p (3686)->p ψ 3C for p (3686)->p ψ 4C for

FIG. 1: Comparison of the invariant mass M (p¯p) between 3C and 4C kinematic fits. For ψ(3686) →

γηc(2S), the open and filled circles are corresponding to 3C and 4C, and for ψ(3686) → p¯p, the

solid and dashed lines are for 3C and 4C, respectively.

π0p is generated to determine the efficiencies of the γp¯p selection (ε

γp¯p) and the π0p¯p

selection (επ0pp¯). The selected π0p¯p events corrected by the efficiencies (εγp¯pπ0p) are taken as the π0p background in ψ(3686) → γp¯p. The shape of this background can be described

with a Novosibirsk function [16] as shown in Fig. 2.

) 2 ) (GeV/c p M(p 3.3 3.35 3.4 3.45 3.5 3.55 3.6 3.65 3.7 ) 2 Events/ (5 MeV/c 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 ) 2 ) (GeV/c p M(p 3.3 3.35 3.4 3.45 3.5 3.55 3.6 3.65 3.7 ) 2 Events/ (5 MeV/c 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

FIG. 2: The measured background from ψ(3686) → π0p¯p for the ψ(3686) → γp¯p mode. The curve

shows the fit with a Novosibirsk function.

For ψ(3686) → π0h

c → π0p¯p, the main background sources are the decays ψ(3686) →

γχcJ, χcJ → p¯p (where J = 1, 2) combined with a fake photon and the π0p¯p decay from

ψ(3686) or continuum process. The χcJ backgrounds are strongly suppressed by using the

3C kinematic fit, where the momentum of the photon with lower energy is allowed to float. For the χcJ backgrounds, the M(p¯pγhigh) (where γhigh is the photon with higher energy)

with 3C peaks at 3.686 GeV/c2, while for the h

c signal, it is below 3.66 GeV/c2 as shown

in Fig. 3 [15]. A requirement M(p¯pγhigh) < 3.66 GeV/c2 is used to remove this background

effectively. The π0p background from the continuum process is studied with the data

sample taken at √s = 3.65 GeV and is found not peaking in the signal region. The π0p

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background having the same final state as signal events is irreducible. It is included in the fit to the M(p¯p) spectrum.

) 2 (GeV/c high γ p p M 3.58 3.6 3.62 3.64 3.66 3.68 3.7 ) 2 Events/(2 MeV/c 0 100 200 300 400 500 600 700 c h 0 π (3686)-> ψ 3C for c h 0 π (3686)-> ψ 4C for c1 χ γ (3686)-> ψ 3C for c1 χ γ (3686)-> ψ 4C for

FIG. 3: Comparison of the invariant mass M (p¯pγhigh) between 3C and 4C kinematic fits. For

ψ(3686) → π0hc, the open and filled circles are corresponding to 3C and 4C, and for ψ(3686) →

γχc1, the solid and dashed lines are for 3C and 4C, respectively.

IV. DETERMINATION OF YIELDS

Figure 4 shows the p¯p invariant-mass distribution for the selected γp¯p candidates. There are clear χc0, χc1, χc2 and ψ(3686) → p¯p peaks. The signal for ηc(2S) → p¯p is not

sig-nificant. An unbinned maximum likelihood fit to the M(p¯p) distribution is used to de-termine the signal yields of ηc(2S) and χcJ. The fitting function is composed of signal

and background components, where the signal components include ηc(2S) and χcJ, and the

background components include π0p, ψ(3686) → p¯p, ψ(3686) → γ

FSRp¯p and nonresonant

background. The line shapes for ηc(2S) and χcJ are obtained from MC simulation following

E3

γ × BW (m; m0, Γ) × fdamp(Eγ), where m is the invariant mass of p¯p, m0 and Γ are the

mass and width of the Breit-Wigner line shape for ηc(2S) and χcJ, and the values are fixed

at the nominal values [3]. Eγ which equals to (m2ψ(3686)− m2)/2mψ(3686) is the energy of the

transition photon in the rest frame of ψ(3686), and fdamp(Eγ) is a function that damps the

diverging tail originating from the E3

γ dependence at the low mass side (corresponding to

high energy of the radiative photon). The form of the damping factor was introduced by the KEDR collaboration and is fdamp(Eγ) =

E2 0

EγE0+(Eγ−E0)2 [18], where E0 is the peak energy of the transition photon. The π0p background is described with a Novosibirsk function with

the fixed shape and amplitude as described earlier. The backgrounds from ψ(3686) → p¯p and ψ(3686) → p¯pγFSR are described with a shape based on a MC simulation, where the

FSR photon is simulated with PHOTOS [19], and their magnitudes are allowed to float. The shape of the nonresonant background is determined from a MC simulation while its magnitude is allowed to float. To account for a possible difference in the mass resolution between data and MC simulation, a smearing Gaussian function G(µ, σ) is convolved with the line shape of χcJ, and the parameters of this function are free in the fit. Since we find

that the discrepancy in the mass resolution decreases with increasing M(p¯p) and is close

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to zero in the ηc(2S) region, a MC-determined line shape is directly used for the ηc(2S) in

the fit to data. The fitting results are shown in Fig. 4. The signal yields of χc0, χc1, χc2,

and ηc(2S) are 1222 ± 39, 453 ± 23, 405 ± 21 and 34 ± 17, respectively. The statistical

significance of the ηc(2S) signal is 1.7σ. The goodness of fit is χ2/ndf = 50.8/65, which

indicates a reasonable fit.

Since ηc(2S) signal is not significant, we determine the upper limit on the number of signal

events. The probability density function (PDF) for the expected number of signal events is taken to be the likelihood in fitting the M(p¯p) distribution while scanning the number of ηc(2S) signal events from zero to a large number, where the signal yields of the χcJ are

free. The 90% C.L. upper limit on the number of signal events Nup, which corresponds to

RNup 0 PDF(x)dx/ R∞ 0 PDF(x)dx = 0.9, is 54. ) 2 ) (GeV/c p M(p 3.3 3.35 3.4 3.45 3.5 3.55 3.6 3.65 3.7 ) 2 Events/ (5 MeV/c 1 10 2 10 3 10 4 10 ) 2 ) (GeV/c p M(p 3.3 3.35 3.4 3.45 3.5 3.55 3.6 3.65 3.7 ) 2 Events/ (5 MeV/c 1 10 2 10 3 10 4 10 data Fitting results (2S) c η , cJ χ p (3686)-> p ψ background 0 π non-resonant process

FIG. 4: The p¯p invariant-mass spectrum after a 3C kinematic fit for selected ψ(3686) → γp¯p

candidates from data. Dots with error bars are data, the blue solid curve is the fitting result,

the red long-dashed line is for the χcJ and ηc(2S) signals, the green long-dash-dotted line is for

ψ(3686) → p¯p, the pink dash-double-dotted line is the contribution of ψ(3686) → π0p¯p and the

cyan dashed line is for the non-resonant process.

Figure 5 shows the p¯p invariant-mass distribution for the selected ψ(3686) → π0p

can-didates. There is no obvious hc → p¯p signal. The signal yield of hc is determined from an

unbinned maximum-likelihood fit to the M(p¯p) distribution in ψ(3686) → π0p with the

signal and the π0p background components. The h

c signal is described by the MC

deter-mined shape convolved with a smearing Gaussian. In the MC simulation, the mass and width of hc are set to the measured values [3]. The smearing Gaussian is used to account

for the difference in the mass resolution between data and MC simulation. The parameters of the Gaussian function are determined from ψ(3686) → π0J/ψ → π0p. The π0p

back-ground is described by an ARGUS function [17] with the magnitude and shape parameters floated. No obvious hc signal event is observed. The upper limit at the 90% C.L. on the

hc → p¯p signal events, calculated with the same method as was applied for the ηc(2S), is

4.4. Figure 5 shows the fitting result with the background shape, and the goodness of fit is χ2/ndf = 18.4/14.

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) 2 ) (GeV/c p M(p 3.46 3.48 3.5 3.52 3.54 3.56 ) 2 Events/ (2 MeV/c 0 2 4 6 8 10 12 14 ) 2 ) (GeV/c p M(p 3.46 3.48 3.5 3.52 3.54 3.56 ) 2 Events/ (2 MeV/c 0 2 4 6 8 10 12 14

FIG. 5: The p¯p invariant-mass spectrum for ψ(3686) → π0p¯p. Dots with error bars are data, and

the blue solid curve is the fitting result with the background shape.

V. SYSTEMATIC UNCERTAINTIES

In the branching-fraction measurements, there are systematic uncertainties from MDC tracking (1% per track) [20], particle identification (1% per track) [20], photon reconstruction (1% per photon) [21], the total number of ψ(3686) events (0.8%) [9], the kinematic fit, and the simulation of helicity angular distribution of the proton and antiproton. The uncertainty in the kinematic fit comes from the inconsistency between the data and MC simulation of the track-helix parameters. We make corrections to the helix parameters according to the procedure described in Ref. [22], and take the difference between the efficiencies with and without the correction as the systematic error. The helicity angular distribution of protons from χcJ is taken from measured data and fitted by the formula 1 + α cos2θ. The α values

for χc0, χc1 and χc2 are 0.09 ± 0.11, 0.12 ± 0.20, and −0.26 ± 0.17, respectively. The selection

efficiencies are determined from MC where the α values are set to the mean values. The change in efficiency by varying the α value by ±1σ is taken as the uncertainty in the proton angular distribution. For ηc(2S)/hc → p¯p, the differences in efficiencies for MC samples

simulated with phase space and 1 + cos2θ, 0.8% and 0.5% for η

c(2S) and hc, respectively,

are taken as the systematic errors.

For the B(ηc(2S)/χcJ → p¯p) measurement, the uncertainties in the fitting procedure

include the damping factor, fitting range, the description of the π0background, and the mass

resolution of M(p¯p). An alternative damping function exp(−E2

γ/8β2) was used by CLEO

[23], where β = 65.0 ± 2.5, and 97 ± 24 MeV for ηc(2S) and χcJ, respectively [22]. The

difference in the final results caused by the two damping factors is taken as the systematic uncertainty. The uncertainty caused by the fitting range is obtained by varying the limits of the fitting range by ±0.05 GeV/c2. The uncertainty of the π0 background is estimated

by varying the parameters of the shape and magnitude by ±1σ. The uncertainty from the resolution of M(p¯p) is found to be negligible.

For B(hc → p¯p), additional uncertainties are caused by the mass resolution of M(p¯p), the

fitting range, the π0 mass requirement and the background shape. The uncertainty from the

mass resolution of M(p¯p) is estimated by varying the resolution by ±1σ. The uncertainty due to the fitting range is estimated by allowing the fitting range to vary within 0.05 GeV/c2. The

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TABLE I: Summary of the relative systematic uncertainties in B(χcJ → p¯p), B(ηc(2S) → p¯p) and B(hc → p¯p) (in %). Source χc0 χc1 χc2 ηc(2S) hc Tracking efficiency 2.0 2.0 2.0 2.0 2.0 Photon detection 1.0 1.0 1.0 1.0 2.0 Particle identification 2.0 2.0 2.0 2.0 1.0 Kinematic fit 0.4 0.2 0.6 1.1 1.4 Total number of ψ(3686) 0.8 0.8 0.8 0.8 0.8 Damping factor 1.1 0.1 0.2 11.8 -Fitting range 1.4 0.4 0.2 5.9 3.4 Background shape 0.8 0.9 0.6 8.9 12.5

Proton angle distribution 0.8 0.6 0.3 0.8 0.5

Resolution of M (p¯p) - - - - 5.7

π0 mass region cut - - - - 3.0

Sum 3.8 3.3 3.2 16.3 14.9

difference in the number of hc signal events is taken as the systematic error. The uncertainty

due to the π0 mass requirement is studied using the decay ψ(3686) → π0π0J/ψ, J/ψ → l+l

[27], and 3% is quoted as the systematic uncertainty. The uncertainty from the background shape (12.5%) is estimated by changing the background shape from an ARGUS function to a second-order polynomial. Table I summarizes all the systematic uncertainties. The overall systematic uncertainties are obtained by summing all the sources of systematic uncertainties in quadrature, assuming they are independent.

VI. RESULTS AND DISCUSSION

We use MC-determined efficiencies to calculate the product branching fractions B(ψ(3686) → γχcJ) × B(χcJ → p¯p). By combining the measurements of B(ψ(3686) →

γχcJ) [3], the branching fractions for χcJ → p¯p are obtained. The results are

summa-rized in Table II. The upper limits on the product branching fractions of the ηc(2S) and

hc are calculated with the formula N

up

Ntot×ε×(1−σ). Here N

up is the upper limit of signal

events, Ntot is the number of ψ(3686) events, ε is the MC-determined efficiency (45.6% for

ψ(3686) → γηc(2S), ηc(2S) → p¯p, and 37.7% for ψ(3686) → π0hc, hc → p¯p), and σ is the

overall systematic error. We obtain B(ψ(3686) → γηc(2S)) × B(ηc(2S) → p¯p) < 1.4 × 10−6

and B(ψ(3686) → π0h

c) × B(hc → p¯p) < 1.3 × 10−7 at the 90% C.L..

The branching fraction for ηc(2S) → p¯p is determined by multiplying the ratio of the

product branching fractions B(ψ(3686)→γηc(2S))×B(ηc(2S)→p¯p)

B(ψ(3686)→γηc(2S))×B(ηc(2S)→K ¯Kπ) and B(ηc(2S) → K ¯Kπ). Here

the product branching fraction B(ψ(3686) → γηc(2S)) × B(ηc(2S) → K ¯Kπ) is taken from

the recent BESIII measurement [24], and B(ηc(2S) → K ¯Kπ) was measured by BABAR [25].

This allows some systematic errors, such as errors in the tracking efficiency and the damp-ing factor, to cancel out. The result is inflated by a factor 1/(1 − σ), where the fractional systematic error σ is dominated by the B(ηc(2S) → K ¯Kπ) measurement. The 90% C.L.

upper limit is determined to be B(ηc(2S) → p¯p) < 4.8 × 10−3. By combining the BESIII

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TABLE II: The selection efficiencies, signal yields extracted from the fit, the product branching

fractions B(ψ(3686) → γχcJ) × B(χcJ → p¯p) and the branching fractions B(χcJ → p¯p). Here the

first errors are statistical and the second systematic.

Channels ε(%) Nsignal B(ψ(3686) → γχcJ) × B(χcJ → p¯p)(×105 ) B(χcJ→ p¯p)(×10−5) χc0 48.5 1222±39 2.37 ± 0.08 ± 0.09 24.5 ± 0.8 ± 1.3 χc1 53.8 453 ± 23 0.79 ± 0.04 ± 0.03 8.6 ± 0.5 ± 0.5 χc2 52.0 405 ± 21 0.73 ± 0.04 ± 0.03 8.4 ± 0.5 ± 0.5 measurement of B(ψ(3686) → π0h

c) [27], the upper limit of the branching fraction is

ob-tained to be B(hc → p¯p) < 1.7 × 10−4 at the 90% C.L., where the errors are treated with

the same method as in B(ηc(2S) → p¯p).

In summary, with a sample of 1.06×108ψ(3686) events, we search for the decays ηc(2S) →

p¯p and hc → p¯p, but no significant signals are observed. The 90% C.L. upper limits of the

branching fractions for ηc(2S) → p¯p and hc → p¯p are determined. The current upper limit

of B(ηc(2S) → p¯p), which is larger than the measurement of B(ηc → p¯p) [26], cannot directly

test the conjecture of Ref. [8] to validate the helicity theorem. The upper limit on B(hc → p¯p)

obtained from this work is consistent with the earlier experimental results [4] and is lower than the predictions [5, 6], where model parameters may need to be tuned. The branching fractions of χcJ → p¯p are measured with improved precision, consistent with the most

recent measurement by CLEO-c [28], and the results are also compatible with theoretical calculation of B(χcJ → p¯p) (J = 0, 1, 2) by including the color octet contribution [29]. The

results presented in this paper will be of interest for future experiments like PANDA in their search for hadronic resonances [30].

VII. ACKNOWLEDGMENTS

The BESIII collaboration thanks the staff of BEPCII and the computing center for their strong support. This work is supported in part by the Ministry of Science and Technol-ogy of China under Contract No. 2009CB825200; National Natural Science Foundation of China (NSFC) under Contracts No. 10625524, No. 10821063, No. 10825524, No. 10835001, No. 10935007, No. 11125525, and No. 11235011; Joint Funds of the National Natural Science Foundation of China under Contracts No. 11079008 and No. 11179007; the Chinese Academy of Sciences (CAS) Large-Scale Scientific Facility Program; CAS under Contracts No. KJCX2-YW-N29 and No. KJCX2-YW-N45; 100 Talents Program of CAS; German Research Foundation DFG under Collaborative Research Center Contract No. CRC-1044; Istituto Nazionale di Fisica Nucleare, Italy; Ministry of Development of Turkey under Con-tract No. DPT2006K-120470; U. S. Department of Energy under ConCon-tracts No. DE-FG02-04ER41291, No. DE-FG02-05ER41374, No. DE-FG02-94ER40823, and No. DESC0010118; U.S. National Science Foundation; University of Groningen (RuG) and the Helmholtzzen-trum fuer Schwerionenforschung GmbH (GSI), Darmstadt; and WCU Program of National

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Research Foundation of Korea under Contract No. R32-2008-000-10155-0.

[1] E. Eichten, S. Godfrey, H. Mahlke and J. L. Rosner, Rev. Mod. Phys. 80, 1161 (2008). [2] S. J. Brodsky and G. P. Lepage, Phys. Rev. D 24, 2848 (1981).

[3] J. Beringer et al. (Particle Data Group), Phys. Rev D 86, 010001 (2012). [4] M. Andreotti et al. Phys. Rev. D 72, 032001 (2005).

[5] X. H. Liu and Q. Zhao, J. Phys. G 38, 035007 (2011).

[6] S. Barsuk, J. He, E. Kou and B. Viaud, Phys. Rev. D 86, 034011 (2012). [7] F. Murgia, Phys. Rev. D 54, 3365 (1996).

[8] K. -T. Chao, Y. -F. Gu and S. F. Tuan, Commun. Theor. Phys. 25, 471 (1996). [9] M. Ablikim et al. (BESIII Collaboration), Chin. Phys. C 37 063001 (2013).

[10] M. Ablikim et al. (BESIII Collaboration), Nucl. Instrum. Meth. A 614, 345 (2010).

[11] S. Jadach, B. F. L. Ward and Z. Was, Comp. Phys. Commu. 130, 260 (2000); Phys. Rev. D

63, 113009 (2001).

[12] http://www.slac.stanford.edu/∼lange/EvtGen; R. G. Ping et al., Chinese Physics C 32, 599 (2008).

[13] J. C. Chen, G. S. Huang, X. R. Qi, D. H. Zhang and Y. S. Zhu, Phys. Rev. D 62, 034003 (2000).

[14] S. Agostinelli et al. (geant4 Collaboration), Nucl. Instrum. Meth. A 506, 250 (2003). [15] M. Ablikim et al. (BESIII Collaboration), Phys. Rev. D 84, 091102 (2011).

[16] The Novosibirsk function is defined as f (mES) = ASexp(−0.5 ln2[1+Λτ ·(mES−m0)]/τ2+τ2),

where Λ = sinh(τ√ln 4)/(στ√ln 4), the peak position is m0, the width is σ, and τ is the tail

parameter.

[17] H. Albrecht et al. (ARGUS Collaboration), Phys. Lett. B 241 (1990) 278. [18] V. V. Anashin et al. Int. J. Mod. Phys. Conf. Ser. 02, 188 (2011).

[19] E. Barberio and Z. Was, Comput. Phys. Commun. 79, 291 (1994).

[20] M. Ablikim et al. (BESIII Collaboration), Phys. Rev. D 86, 032014 (2012) [21] M. Ablikim et al. (BESIII Collaboration), Phys. Rev. D 83, 112005 (2011) [22] M. Ablikim et al. (BESIII Collaboration), Phys. Rev. D 87, 012002 (2013) [23] R. E. Mitchell et al. (CLEO Collaboration), Phys. Rev. Lett. 102, 011801 (2009). [24] M. Ablikim et al. (BESIII Collobration), Phys. Rev. Lett. 109, 042003 (2012). [25] B. Aubert et al. (BaBar Collaboration), Phys. Rev. D 78, 012006 (2008). [26] M. Ablikim et al. (BESIII Collaboration), Phys. Rev. D 86, 092009 (2012). [27] M. Ablikim et al. (BESIII Collaboration), Phys. Rev. Lett. 104, 132002 (2010). [28] P. Naik et al. (CLEO Collaboration), Phys. Rev. D 78, 031101(R) (2008). [29] S. M. H. Wong, Eur. Phys. J. C14, 643 (2000).

[30] A. Lundborg, T. Barnes and U. Wiedner, Phys. Rev. D 73, 096003 (2006).

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